C₁₁×#13565 #14590758

order	2816
nilpotency class	5
isoclinism	isoclinic class of #13561
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13565

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	C₂×AΣL(1,𝔽₁₆)
commutator	C₂×D₄	C₂²×C₄×C₁₁
Frattini, cosocle	#124	C₂³×C₁₁
prime radical	C₂×C₁₁×H(5,𝔽₂)	C₄
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#124 ◁ G

496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,20,17,22,29,38)(14,23,25,36,24,39,40,43)(16,21,32,37,31,19,28,35)(18,27,34,30,33,41,42,26);(12,14)(13,18)(15,27)(16,30)(17,24)(19,23)(20,36)(21,39)(22,33)(25,32)(26,31)(28,40)(29,41)(34,37)(35,42)(38,43);(14,24)(18,33)(23,39)(25,40)(26,30)(27,41)(34,42)(36,43)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6553);